**Casio fx-CG50 and TI-84 Plus CE: Multilinear Regression with Correlation**

**Introduction**

The program MULT2LIN calculates multiple linear regression with 2 independent variables x_1 and x_2 and correlation of the data. The data will be used to fit the plane:

y = b + a_1 * x_1 + a_2 * x_2

by least squares.

The correlation is a calculated by:

R = √(( Y^2 + Z^2 – 2 * X * Y * Z) / (1 – X^2))

where:

Y = correlation between x_1 and y

Z = correlation between x_2 and y

X = correlation between x_1 and x_2

The general correlation between two variables (x,y) is calculated by:

r = ( n * Σxy – Σx * Σy ) / √( (n * Σx^2 – (Σx)^2) – (n * Σy^2 – (Σy)^2) )

**Casio fx-CG 50 Program MULT2LIN**

This is the text version (MULT2LIN.txt)

‘ProgramMode:RUN

“EWS 2019-08-07”

“MULTILINEAR”

“REGRESSION”

“LIST X1: “?->List 2

“LIST X2: “?->List 3

“LIST Y: “?->List 1

If Dim List 1<>Dim List 2 Or Dim List 1<>Dim List 3

Then

“UNEQUAL LENGTH”DispsStop

IfEnd

LinearReg(a+bx) List 2,List 1

Regression_r->Y

LinearReg(a+bx) List 3,List 1

Regression_r->Z

LinearReg(a+bx) List 2,List 3

Regression_r->X

Sqrt((Y^+Z^-2*X*Y*Z)/(1-X^))->R

“CORRELATION: “RDisps

Dim List 1->Dim List 4

Fill(1,List 4)

List->Mat(List 4,List 2,List 3)->Mat X

List->Mat(List 1)->Mat Y

(Trn Mat X*Mat X)^*Trn Mat X*Mat Y->Mat B

“_Mat _B:”DispsMat B

Notes:

<> is ≠

Disps is ⊿

Sqrt is √

Regression_r can be found by [ VARS ] , (STAT), (GRAPH), ( > ), ( r ). The character r is in bold font.

fx-CG 50 syntax:

LinearReg(a+bx) y data, x data

List->Mat(column list, column list, … )

This is what it would look like on the calculator:

“MULTILINEAR”

“REGRESSION”

“LIST X1: “?->List 2

“LIST X2: “?->List 3

“LIST Y: “?->List 1

If Dim List 1 ≠ Dim List 2 Or Dim List 1 ≠ Dim List 3

Then

“UNEQUAL LENGTH”⊿

Stop

IfEnd

LinearReg(a+bx) List 2,List 1**r**->Y

LinearReg(a+bx) List 3,List 1**r**->Z

LinearReg(a+bx) List 2,List 3**r**->X

√((Y²+Z²-2*X*Y*Z)/(1-X²))->R

“CORRELATION: ” ⊿

Dim List 1->Dim List 4

Fill(1,List 4)

List->Mat(List 4,List 2,List 3)->Mat X

List->Mat(List 1)->Mat Y

(Trn Mat X*Mat X)⁻¹*Trn Mat X*Mat Y->Mat B

“_Mat _B:”⊿

Mat B

**TI-84 Plus CE Program MULT2LIN**

* Can be used on all of the TI-84 and TI-83 family

* This program needs to be typed in

“EWS 2019-08-07”

Disp “MULTLINEAR”,

“REGRESSION”

Input “LIST X1: “, L1

Input “LIST X2: “, L2

Input “LIST Y: “, L3

If (dim(L1) ≠ dim(L2)) or (dim(L1) ≠ dim(L3))

Then

Disp “UNEQUAL LENGTH”

Stop

End

LinReg(ax+b) L1, L3

r → Y

LinReg(ax+b) L2, L3

r → Z

LinReg(ax+b) L1, L2

r → X

√( ( Y² + Z² – 2*X*Y*Z ) / (1 – X²) ) → R

Disp “CORRELATION:”

Pause R

dim(L1) → dim(L4)

Fill(1, L4)

List>matr(L4,L1,L2,[A])

List>matr(L3,[C])

([A]^T * [A])⁻¹ * [A]^T * [C] → [B]

Disp “[B] =”

Pause [B]

Notes:

^T is the transpose

TI-84 Syntax:

LinReg(ax+b) x list, y list

List>Mat(column list, column list, column list, …. , matrix)

**The output of MULT2LIN**

R: correlation of the mutilinear data

A 3 x 1 matrix that represents the coefficients for b + a_1 * x_1 + a_2 * x_2:

[ [ b ]

[ a_1 ]

[ a_2 ] ]

**Example**

A hiring firm collects data on six potential employees based on the criteria:

* Number of years of education (12 = High School Graduate, 16 = 4-Year Degree, 18 = Masters Degree, 20 = Ph.D)

* Number of years of work experience, including part-time and full-time

* Starting salary at a professional firm

Are education and work experience factors to predicting starting salary? Data from 7 employees are taken below:

X1 Data: {12, 12, 14, 16, 15, 18, 20}

X2 Data: {0.5, 2, 1.5, 2, 3, 3.5, 5}

Y Data: {30000, 35000, 35000, 50000, 52000, 64000, 100000}

Results:

Correlation: R = 0.9650583083

Coefficient Matrix:

[ [ -24932.24299 ]

[ 3539.719626 ]

[ 9042.056075 ] ]

The estimate equation is:

y = -24932.24299 + 3539.719626 * x1 + 9042.056075 * x2

x1 = Number of years of education

x2 = Number of years of work experience

Source:

Higgins, Jim Ed. D. “Chapter 4: Introduction to Multiple Regression” Excerpt from the Radical Statistician 2005. http://www.biddle.com/documents/bcg_comp_chapter4.pdf Retrieved August 6, 2019

Eddie

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